Problem: The following line passes through point $(-2, -8)$ : $y = -\dfrac{7}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-2, -8)$ into the equation gives: $-8 = -\dfrac{7}{4} \cdot -2 + b$ $-8 = \dfrac{7}{2} + b$ $b = -8 - \dfrac{7}{2}$ $b = -\dfrac{23}{2}$ Plugging in $-\dfrac{23}{2}$ for $b$, we get $y = -\dfrac{7}{4} x - \dfrac{23}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${14}$ ${15}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ ${\llap{-}14}$ ${\llap{-}15}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${14}$ ${15}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ ${\llap{-}14}$ ${\llap{-}15}$ $(-2, -8)$